Received: by alpheratz.cpm.aca.mmu.ac.uk id CAA15438 (8.6.9/5.3[ref pg@gmsl.co.uk] for cpm.aca.mmu.ac.uk from fmb-majordomo@mmu.ac.uk); Tue, 5 Feb 2002 02:46:31 GMT Date: Mon, 4 Feb 2002 18:40:47 -0800 Message-Id: <200202050240.g152elf14217@mail13.bigmailbox.com> Content-Type: text/plain Content-Disposition: inline Content-Transfer-Encoding: binary X-Mailer: MIME-tools 4.104 (Entity 4.116) X-Originating-Ip: [66.156.195.136] From: "Joe Dees" <joedees@addall.com> To: memetics@mmu.ac.uk Subject: Re: Tipping Point author in town Sender: fmb-majordomo@mmu.ac.uk Precedence: bulk Reply-To: memetics@mmu.ac.uk('binary' encoding is not supported, stored as-is)
>Date: Sat, 2 Feb 2002 17:22:57 -0500
> Re: Tipping Point author in town "Wade T.Smith" <wade_smith@harvard.edu> memetics@mmu.ac.ukReply-To: memetics@mmu.ac.uk
>
>On Friday, February 1, 2002, at 08:59 , Joe Dees wrote:
>
>> Yeah; what is his opinion on the Godelian threshhold for self-reference
>> as a tipping point for the development of self-conscious awareness? A
>> very predictable question from me, ayy?
>
>Well, yes, it is. ;-)
>
>OK, for the moment, let's assume he will have no idea what the Godelian
>threshold is- could you send me a nicely phrased, quickly asserted,
>question I could rehearse and learn?
>
>All the while realizing that I will be among a group of remarkable
>miscellany, as I'm sure you're aware.
>
Godel's Incompleteness Theorems I and II are the most important in 20th century mathematics. It is asserted that beyond a certain level of complexity, that any axiomatic system contains undecideable statements; the reason for this is the emergence of self-reference in complex systems. Let's postulate axiomatic system A, and state that all true statements, and only true statements, are inside A. Now let us construct statement B. B is recursive and self-referential; that is, it refers to its own relation with axiomatic system A, and what it contends is that "B is not an axiom of A". What has happened here? If we include B in A, then B contains the false statement that B is not an axiom of A, and thus does not contain only true statements, but if we exclude B from A, then A does not contain all true statements, for it does not include the true statement that B is not an axiom of A. To put it plainly, B either belongs BOTH inside and outside A, or NEITHER inside nor outsi!
de A, and the dilemma is unresolveable within system A. B is undecideable with reference to A. The bottom drops out; mathematics is revealed as a Zen koan.
But in reference to the universe A, WE are B, for we are within a universe that we nevertheless entertain a perspectival (point of) view upon; in other words, Krishnamurti notwithstanding, as far as self-conscious awareness within our environs goes, we are at once NOT and NOT-NOT the world ("Neti, neti." (Not this, not that). Mind and world are not one, not two, not many, but are components od a dynamic and recursive interrelational system.
hope this helps.
>
>- Wade
>
>
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This was distributed via the memetics list associated with the
Journal of Memetics - Evolutionary Models of Information Transmission
For information about the journal and the list (e.g. unsubscribing)
see: http://www.cpm.mmu.ac.uk/jom-emit
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